Let z € C, r> 0 and a(z,r) := z+re", t e [0,27]. Calculate the following integrals: a) Jai.1) * dz; b) Sasi.1) dz; c) fa(-22) dz; d) Sao.10) dz; e) Sa(0.10) EE-T) tiz dz.

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

A:

Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: VIII. Let f(x,y,z) = xe" +z? and F(x,y,z) = (xy, x²yz, yz). Compute 1. Div(grad(f)) 2. Div(curl(f))…

A:

Q: Is the following statement correct? The differential equation y' = (x² + y²)z has a unique solution…

A:

Q: 4. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1,4,9). C

A: We have to find the line integral  ∫C xeyz ds ,  where C is the line segment from (0, 0, 0) to (1,…

Q: -(1,2,3) What should m be for the integral S00 (2xyz? + 3)dx + (mx²z³ – 2)dy + (3x²yz² + 4z)dz to be…

A: The curl of a conservative field, F→ is 0→ . In that case, the line integral of F→ is path…

Q: Find paromet ric aquation of Line L where to paiut A(Xmiya) is and

A:

Q: 1. Evaluate by using a contour integral method sins i) f'{- Vs

A: The given integral: This can be rewritten as, Contour integration:        It is the process of…

Q: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: u? du u+2 b)

A:

Q: () 4 dædydz; V: {r+y+ z = 3; x 20; y 20; :> 0} O A. pi В. 3 С. б D. 9

A: The given integral is ∫∫∫V43-xdxdydz and region is x+y+z=3; x≥0 ,y≥0, z≥0

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: The Definite Integral as Area (x) dr 2. J Ax) dr 3. J Ax) dx 1. S M:x) dr 5. JAx) dx S Mx) dr 4. 6.…

A:

Q: V11 10) (z-VT) dz 15 15 A) - V C) - V1ī D) -VIT 11 11 2 В) + 21 2 11) (2x2 + x + 4) dx X + 1125 A) -…

A: We have to integrate

Q: ²²-i)² dx 2³+dz when the contour C is the circle |z − 21 = 5 +4 1 Z- COSZ Cosz, dz when the contour…

A: According to the guidelines only three subparts should be answered. Therefore to answer the rest of…

Q: sin z dz, C (z+1)7 tan (z/2) ii) J. dz C Z-T/2

A: To Solve the above integral we use Cauchy Integral Formula.Given in Second Step.

Q: DO NOT include spaces in between characters. * d (y -8 de (y° +8 Compute at x =2.

A:

Q: 耳 ixn=wyr Show that d P

A: Given a function is two variables.

Q: Given that | (3 + 4)' da, find an equivalent definite integral in terms of u. 1 a) О u' da u da b) O…

A:

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: y A. A' B' 6 54 123 4 5 6 2 C

A: given diagram is

Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: 1. Evaluate the integral b) (xidx c) J√x dx

A: We are authorized to answer three subparts at a time, so we are answering the first three subparts,…

Q: 2. Rewrite the integral f(x, y, z)dzdxdy using the order dxdydz.

A:

Q: Evalute the following int egrals: i) s sintx cos"x dx ii) SV-4x? dre cosx Sin sん x v) Sde Vax+6X+2…

A: According to our terms and condition i am solving first part.for other parts please reppst.

Q: 18. Sx²Vx3 – 4 dx a) Let u =x^3-4 b) Find du c) Find dx d) Evaluate the integral…

A: a) Let u=x3-4So, du=3x2dxor, dx=du3x2

Q: Let A = {1, 2,...,: 10}. Find the closure and the interior of A in the following topo- logical…

A: In mathematics, topology is the study of the properties of spaces that are preserved under…

Q: Q6:-Find aw and ar if as 1) W = x2 + y² 2) W = Ln(x² + y² + 2 ,x = %3D

A: It is partial derivative

Q: 6. dyda ydyda 2R Sys of 37 15D to

A: Formula Used:-(1) ∫a2-x2=xa2-x22+a22sin-1(xa)+c(2) ∫xa2-x2 dx=-(a2-x2) 323Consider,A=∫02R∫0R2-(x-R)2…

Q: et z e C, r>0 and a(z,r) := z + re", te [0,27]. Calculate the following integrals: a) Saça.1) dz; b)…

A: According to our guideline, we can solve first three subpart of a multipart question.kindly repost…